The D.C. Department of Corrections identified the man as 51-year-old Deon Crowell in a letter sent to the staff.
They say he died Monday morning.
There are 80 new cases of COVID-19 in the District – bringing the total to 1,955.
Fifty-two people in D.C. have now died as a result of the novel coronavirus.
The mayor also announced on Monday that D.C. has set up a hotline for residents who are in need of help, but are homebound because of COVID-19.
The number for the hotline is 1-888-349-8323, and you can also reach officials online at https://coronavirus.dc.gov/gethelp.
The District also closed roads to traffic on Beach Drive in Rock Creek Park and roads in Anacostia Park and Fort Dupont Park through April 30.
Bowser noted that the closures will give residents more spaces for “essential” exercise.